The use of bent crystals with high integrated reflectivity in focusing crystal spectrometers (Johann and von Hamos schemes) is considered. It is shown that in a von Hamos scheme mosaic focusing takes place. Thus a mosaic crystal simultaneously provides high spectral resolution and high efficiency. Expressions for the mosaic focusing are obtained. Focusing mica and graphite crystal von Hamos spectrometers (radius of crystal curvature is 20 mm) are investigated: spectral and spatial resolution and absolute efficiency are measured in a spectral range of 2 - 2.6 angstroms using laser-produced plasma and iron isotope x-ray sources. The mica crystal spectrometer showed high spatial (up to 10 micrometers ) and spectral ((lambda) /(delta) (lambda) approximately 1000) resolution, whereas the graphite spectrometer showed very high efficiency (30 - 70 times higher than the mica crystal) and moderate spectral resolution ((lambda) /(delta) (lambda) approximately 500 - 750). In the latter case mosaic focusing is observed: spectral resolution is 10 - 15 times higher than spectral resolution determined by the mosaic spread of the crystal ((lambda) /(delta) (lambda) approximately 50). The results allow one to estimate a maximum efficiency for focusing crystal spectrometers. Prospects for using the von Hamos spectrometers for x-ray spectroscopy and x-ray fluorescence are considered.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.